Fractional Brownian motion analysis for epidemic spreading of diseases

In this paper, we use the nonlinear fractional stochastic differential equation approach with Hurst parameter $H$ into the range $1/2< H< 1$ to perform the statistical analysis of public data of number of infected by coronavirus in countries where the number of cases is larger as Brazil and India. We analyze the rises and falls of novel daily cases of coronavirus, where the fluctuation in the official data is treated as a random term in the stochastic differential equation for the fractional Brownian motion. The projection of novel cases in the future is treated as quadratic mean deviation in the official data of novel cases daily since the beginning of the pandemic up the present. Additionally, statistical tests as skewness and kurtosis are performed with aim to estimate the shape of the probability density distribution of novel cases in long time, since the beginning of pandemic, in tentative to estimate the behavior of novel cases in the future.